Average Error: 15.1 → 0.9
Time: 15.2s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}
double f(double g, double a) {
        double r6723352 = g;
        double r6723353 = 2.0;
        double r6723354 = a;
        double r6723355 = r6723353 * r6723354;
        double r6723356 = r6723352 / r6723355;
        double r6723357 = cbrt(r6723356);
        return r6723357;
}
↓
double f(double g, double a) {
        double r6723358 = g;
        double r6723359 = cbrt(r6723358);
        double r6723360 = 1.0;
        double r6723361 = 2.0;
        double r6723362 = a;
        double r6723363 = r6723361 * r6723362;
        double r6723364 = cbrt(r6723363);
        double r6723365 = r6723360 / r6723364;
        double r6723366 = r6723359 * r6723365;
        return r6723366;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.1

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied cbrt-div0.9

    \[\leadsto \color{blue}{\frac{\sqrt[3]{g}}{\sqrt[3]{2 \cdot a}}}\]
  4. Using strategy rm

  5. Applied div-inv0.9

    \[\leadsto \color{blue}{\sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}}\]

  6. Final simplification0.9

    \[\leadsto \sqrt[3]{g} \cdot \frac{1}{\sqrt[3]{2 \cdot a}}\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  (cbrt (/ g (* 2 a))))